A. \(2\).
B. \(6\).
C. \(8\).
D. \(4\).
LỜI GIẢI CHI TIẾT
Theo đề bài ta có: \(S = 5 \Leftrightarrow \int\limits_0^1 {f’\left( x \right)} dx – \int\limits_1^3 {f’\left( x \right)} dx = 5 \Leftrightarrow \left. {f\left( x \right)} \right|_0^1 – \left. {f\left( x \right)} \right|_1^3 = 5\)
\( \Leftrightarrow f\left( 1 \right) – f\left( 0 \right) – \left( {f\left( 3 \right) – f\left( 0 \right)} \right) = 5 \Leftrightarrow 2f\left( 1 \right) – f\left( 0 \right) = 4\)
Xét \(\int\limits_0^1 {\left( {x + 1} \right)} f’\left( x \right)dx = 2\)
Đặt: \(\left\{ {\begin{array}{*{20}{c}}{u = x + 1}\\{dv = f’\left( x \right)dx}\end{array}} \right. \Rightarrow \left\{ {\begin{array}{*{20}{c}}{du = dx}\\{v = f\left( x \right)}\end{array}} \right.\)
Suy ra:\(\left. {\left( {x + 1} \right)f\left( x \right)} \right|_0^1 – \int\limits_0^1 {f\left( x \right)} dx = 2 \Leftrightarrow 2f\left( 1 \right) – f\left( 0 \right) – \int\limits_0^1 {f\left( x \right)} dx = 2 \Leftrightarrow \int\limits_0^1 {f\left( x \right)} dx = 2\)
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